With the score at 1-0, Daniel Agger was shown a straight red card for bringing down Shane Long in the penalty area and, although the resulting spot kick was saved, the Reds conceded another three minutes later when Long was brought down by Martin Skrtel.
"The sending-off and penalties were very, very harsh I felt," Rodgers told BBC Sport. "Some of the decisions went against us. We will have more days like this along the way, that is the reality, but I could not ask many more from the players.
"They have given me everything. We had some chances but West Brom took full advantage of the extra man.
"There were some good moments today but it was a day when everything went against us really. We just have to move on."
Liverpool's next Premier League fixture is at home to Manchester City a week tomorrow.